This invention relates to a method and an apparatus for placing in readiness fiber bales, such as cotton, chemical fiber or other bales in a series, in preparation for a fiber tuft removal process performed by a travelling bale opener. One or several successive initial fiber bales of the series are positioned at a slight inclination in one direction whereas the additional bales of the series are positioned either in a vertical orientation or at an inclination which is opposite to the inclination of the initial fiber bale or fiber bales. Prior to positioning the additional fiber bales, the initial fiber bale or fiber bales are held (stabilized) by a bale holding and/or supporting device as described in the parent application Serial No. 07/936,702. After the additional fiber bales have been deposited and, as they lean against an adjoining initial fiber bale, they themselves are capable of stabilizing the initial fiber bales. Therefore, the holding and/or supporting device is moved away from the initial fiber bale or fiber bales, that is, as the bale resupplying of the bale series continues, the initial bales no longer need the bale holding and/or supporting device for stabilization.